Dynamic Systems Identification using sparse regression and computer vision

• Grant number: 26/09685-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2026
• End date: June 30, 2027
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Paulo José Paupitz Gonçalves
• Grantee: Gustavo Garcia Alves
• Host Institution: Faculdade de Engenharia (FE). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The identification of nonlinear systems is a challenging task. Unlike linear systems, for which the principle of superposition holds, the response of a nonlinear system depends fundamentally on the excitation levels and on the corresponding system response. The type of excitation applied to a mechanical system is also a crucial factor. For example, harmonic excitations may produce distinct responses even at the same excitation frequency. In this work, a mechanical oscillator with nonlinear behavior is investigated through free vibration. The displacement is captured using computer vision techniques, and the response is estimated by numerical differentiation combined with noise-reduction methods. Two strategies are employed to extract information from the system. The first strategy uses the Hilbert transform to obtain the instantaneous frequency and damping. The second strategy integrates sparsity-promoting methods and machine learning with nonlinear dynamical systems to discover the governing equations from noisy measurement data. The assumption regarding the model structure is that only a few essential terms govern the dynamics, making the equations sparse in the space of possible functions. This hypothesis is generally valid for mechanical systems, such as the Duffing oscillator, for example. Sparse regression is used to determine the minimum set of terms in the dynamic equations required to represent the data accurately. (AU)